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Cohomological Aspects in Complex Non-Kähler Geometry

✍ Scribed by Daniele Angella (auth.)

Publisher
Springer International Publishing
Year
2014
Tongue
English
Leaves
289
Series
Lecture Notes in Mathematics 2095
Edition
1
Category
Library
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✦ Synopsis

In these notes, we provide a summary of recent results on the cohomological properties of compact complex manifolds not endowed with a Kähler structure.

On the one hand, the large number of developed analytic techniques makes it possible to prove strong cohomological properties for compact Kähler manifolds. On the other, in order to further investigate any of these properties, it is natural to look for manifolds that do not have any Kähler structure.

We focus in particular on studying Bott-Chern and Aeppli cohomologies of compact complex manifolds. Several results concerning the computations of Dolbeault and Bott-Chern cohomologies on nilmanifolds are summarized, allowing readers to study explicit examples. Manifolds endowed with almost-complex structures, or with other special structures (such as, for example, symplectic, generalized-complex, etc.), are also considered.

✦ Table of Contents

Front Matter....Pages i-xxv
Preliminaries on (Almost-)Complex Manifolds....Pages 1-63
Cohomology of Complex Manifolds....Pages 65-94
Cohomology of Nilmanifolds....Pages 95-150
Cohomology of Almost-Complex Manifolds....Pages 151-232
Back Matter....Pages 233-264

✦ Subjects

Differential Geometry; Several Complex Variables and Analytic Spaces

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